Scaling properties of the pairing problem in the strong coupling limit

We study the excited states of the pairing Hamiltonian providing an expansion for their energy in the strong coupling limit. To assess the role of the pairing interaction we apply the formalism to the case of a heavy atomic nucleus. We show that only a few statistical moments of the level distribution are sufficient to yield an accurate estimate of the energy for not too small values of the coupling G and we give the analytic expressions of the first four terms of the series. Further, we discuss the convergence radius Gsing of the expansion showing that it strongly depends upon the details of the level distribution. Furthermore Gsing is not related to the critical values of the coupling Gcrit, which characterize the physics of the pairing Hamiltonian, since it can exist even in the absence of these critical points.